A circle has a radius of $6$. An arc in this circle has a central angle of $112^\circ$. What is the length of the arc? ${12\pi}$ ${112^\circ}$ $\color{#DF0030}{\dfrac{56}{15}\pi}$ ${6}$
Solution: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (6) = 12\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{112^\circ}{360^\circ} = \dfrac{s}{12\pi}$ $\dfrac{14}{45} = \dfrac{s}{12\pi}$ $\dfrac{14}{45} \times 12\pi = s$ $\dfrac{56}{15}\pi = s$